Problem-based tasks (PBTs) are math lessons built around a single, compelling problem.

The problems are truly “problematic” for students. A “problematic” problem is challenging and doesn’t offer an immediate solution. This means that a given problem might be problematic for some students but not others. For example, consider the question: “I had five apples and then I ate two of them. How many apples do I have now?” This question may be problematic for a kindergartener, but it isn’t problematic for a first grader who immediately knows to subtract. With problem-based tasks, the problems must be problematic.

The problems provide an opportunity for students to build conceptual understanding. Problem-based tasks require students to apply their current understanding and skills to new contexts that highlight core math concepts. For example, when students solve a problem that could be solved with multiplication before they have formally been taught what multiplication is and how it works, they build an understanding that multiplication is repeated addition.

The problems give all students access to develop understanding. Well-designed problem-based tasks provide multiple entry points for students to engage in problem solving, ensuring that all students have access to the same concepts. When students solve the problems in different ways—including drawing pictures, acting out the problem, writing algorithms, and using manipulatives—they make connections between the variety of models that all accurately illustrate the underlying mathematics.

The idea of centering the classroom environment around problems and students’ ideas about them—as opposed to around the teacher and his or her authority about the mathematics—is rather novel. Students have prior knowledge and experience that they do not have readily available until it is triggered by a problem that relates to the previous one. The problems in a PBL curriculum need to be scaffolded in such a way that students are made ready for what is coming next. If this does not happen, then they will be unable to access their prior knowledge.

It might not take a lot of convincing that this type of teaching directly speaks to many of the practice standards and recommended teaching practices, but for many teachers, it does take convincing that it has value and can be accessible to all students. It also is not as easy as it sounds. Teachers may face many obstacles when moving toward this type of pedagogy, and they need to consider a great deal of assessment and classroom strategies at the same time.

Aspects of Problem-Based Teaching (Schettino 2013)